In public washrooms here most toilets have more water in them than home toilets so skidmarks are less an issue. I would probably try to second flush and that is it.

In a home toilet, I would wipe with paper and second flush. I would even get my hand wet and then wash my hands before leaving a mark. Our low flow toilets at home work pretty well, even though the water level is low the swish of the water is pretty forceful and unless the toilet is left full for hours the swish washes most everything off pretty well.

Also, some public toilets have a swish that might qualify as a minor tsunami, which I imagine also helps.

Jezebel had a great article a while back covering bathroom etiquette, which boiled down to "Leave the bathroom the way you found it".

I think there's a difference between a public, private and shared bathroom.

In a public washroom the facilities are managed by paid staff that hopefully check the room regularly and clean up any messes. No or very little cleaning supplies are available to the average user.

In a private washroom, the facilities are maintained by yourself or your hosts. I'd be mortified to leave a mark behind in my host's toilet and would use whatever was available to clean it up. Likewise, if a guest left a "surprise" for me I'd probably think twice before inviting extra work again.

In a shared washroom, such as an office or a roommate situation, I think people should behave as much like it was a "hosted" washroom as possible. Keep all traces to a minimum at all times. There should be supplies to clean up if needed. Each stall in our shared ladies at work has a toilet brush. That's so you don't have to leave the stall to clean up the low-flow toilet if necessary. I usually give the seat a good wipe and drop the tp in the bowl before starting, ounce of prevention and all that. "If you know you have to go, grab a sheet and lay a row." Or something. I think that was for "unladylike noises".

Another thing the article touched on was little bits of tp on the floor. Not only is it gross to litter, small, white, slippery pieces of paper on slick tile or marble floors can be dangerous. Just pick it up! You're washing your hands anyway, right?